Quarks in the Quark-Gluon Plasma

1
Tokyo Univ., Sep. 27, 2007
Lattice Study of
Quarks in the Quark-Gluon Plasma
Masakiyo Kitazawa (Osaka Univ.)
F. Karsch and M.K., arXiv0708.0299
2
QGP Phase near Tc
RHIC experiments

• strong collective behavior ? perfect fluid?

Lattice simulations

• critical temperature
• energy density
• charmonium spectra

M. Cheng, et al., PRD74,054507 (06). Y. Aoki, et
al., PLB643,46 (06).
Asakawa, Hatsuda, PRL92,012001 (04). Datta,
Karsch, Petreczky, PRD69,094507 (04). Umeda,
Nomura Matsufuru, EPJC39S1,9 (05).
3
Why Quark ?
4
Why Quark ?
Study of property of quark in lattice
Z(p)
vacuum
Bowman, Heller, Williams, Zhang, Coad ,
Leinweber, Furui, Nakajima,
Bowman et al.
M(p)
finite T
a paper and 2 proceedings.

• Boyd, Gupta, Karsch NPB 385,481(92).
• Petreczky, Karsch, Laermann, Stickan, Wetzorke,
  NPPS106,513(02).
• Hamada, Kouno, Nakamura, Saito, Yahiro,
  hep-ph/0610010.

5
Quarks at Extremely High T

• Hard Thermal Loop approx. ( p, w, mqltltT )
• 1-loop (gltlt1)

Klimov 82, Weldon 83 Braaten, Pisarski 89

• Gauge independent spectrum

w / mT
plasmino

• 2 collective excitations
• having a thermal mass

• The plasmino mode has
• a minimum at finite p.

p / mT
6
Decomposition of Quark Propagator
Free quark with mass m
HTL ( high T limit )
7
Decomposition of Quark Propagator
Free quark with mass m
HTL ( high T limit )
8
Quark Spectrum as a function of m0
Quark propagator in hot medium at T gtgtTc
- as a function of bare scalar mass m0
9
Fermion Spectrum in QED Yukawa Model
Baym, Blaizot, Svetisky, 92
Yukawa model
1-loop approx.
Spectral Function for g 1 , T 1
thermal mass mTgT/4
single peak at m0
Plasmino peak disappears as m0 /T becomes larger.
cf.) massless fermion massive boson M.K.,
Kunihiro, Nemoto,06
10
Quark Propagator in Quenched Lattice
quenched approx.
Configurations are distributed with a weight
exp(-SG).
fermion matrix
in continuum
Wilson fermion
We can calculate quark propagator with various
m0 for a given set of gauge(-fixed) configuration!
11
Correlator and Spectral Function
dynamical information
observable in lattice
12
Simulation Setup

• quenched approximation
• clover improved Wilson
• Landau gauge fixing

T b Nt Lattice size
1.5Tc 6.64 12 483x12, 363x12
6.87 16 643x16, 483x16
3Tc 7.19 12 483x12, 363x12
7.45 16 643x16, 483x16

• vary bare quark mass m0
• see only zero momentum p0

configurations generated by Bielefeld
collaboration

• 2-pole approx. for r(w,p0)
• wall source

13
Choice of Source
Whats the source?
Wall source, instead of point source
point
wall
point
t

• same (or, less) numerical cost
• quite effective to reduce noise!!

wall
t
the larger spatial volume, the more effective!
14
Exercise 1 Dirac Structure of C(t )
quark propagator
p0
even odd
15
Exercise 2 C(t ) and r (w )
w
E
0
16
Exercise 2 C(t ) and r (w )
w
E
0
17
Correlation Function
643x16, b 7.459, k 0.1337, 51confs.
t /T

• We neglect 4 points near the source from the fit.
• 2-pole ansatz works quite well!! ( c 2/dof.2 in
  correlated fit)

18
m0 Dependence of C(t )
kc0.13390 in vacuum
m0 small
k 0.134
k 0.132
m0 large
k 0.130
t /T

• Shape of C(t) changes from chiral symmetric
• to single pole structures.

19
m0 Dependence of C(t )
kc0.13390 in vacuum
m0 small
k 0.134
k 0.132
m0 large
k 0.130
t /T

• Shape of C(t) changes from chiral symmetric
• to single pole structures.

20
Spectral Function
T 3Tc 643x16 (b 7.459)
T3Tc
E2
E / T
w m0 pole of free quark
E1
Z2 / (Z1Z2)
m0 / T
21
Spectral Function
T 3Tc 643x16 (b 7.459)
T3Tc
E2
E / T
w m0 pole of free quark
E1
Z2 / (Z1Z2)
m0 / T

• Limiting behaviors for
  are as expected.
• Chiral symmetry of quark propagator restores
  around m00.
• E2gtE1 qualitatively different from the 1-loop
  result.

22
Temperature Dependence
643x16
E2
E / T
E1
Z2 / (Z1Z2)
m0 / T

• mT /T is insensitive to T.
• The slope of E2 and minimum of E1 is much clearer
  at lower T.

23
Lattice Spacing Dependence
T3Tc
E2
643x16 (b 7.459) 483x12 (b 7.192)
E / T
E1
same physical volume with different a.
m0 / T

• No lattice spacing dependence within statistical
  error.

24
Spatial Volume Dependence
T3Tc
E2
643x16 (b 7.459) 483x16 (b 7.459)
E / T
E1
same lattice spacing with different aspect ratio.
m0 / T

• Excitation spectra have clear volume dependence
• even for Ns /Nt 4.

25
Extrapolation of Thermal Mass
Extrapolation of thermal mass to infinite spatial
volume limit
T1.5Tc
mT /T 0.800(15) mT 322(6)MeV
mT /T
1.5Tc
T3Tc
3Tc
643x16
483x16
mT /T 0.771(18) mT 625(15)MeV

• Small T dependence of mT/T,
• while it decreases slightly with increasing T.
• Simulation with much smaller Nt /Ns is desireble.

26
Effect of Dynamical Quarks
Quark propagator in quench approximation
In full QCD,
? screen gluon field ? suppress mT?
? meson loop ? will have strong effect
if mesonic excitations exist
massless fermion massive boson ? 3 peaks in
quark spectrum! M.K., Kunihiro,
Nemoto, 06
27
Summary
Excitations of quark degrees of freedom near but
above Tc have a simple excitation spectrum
having a plasmino mode and mT!
Lattice simulation can successfully analyze it.

• Thermal gluon field gives rise to the thermal
  mass in the light quark spectra.
• The plasmino mode disappears for heavy quarks.
• The ratio mT/T is insensitive to T near Tc.

Puzzles

• different behavior from 1-loop result.
• strong spatial volume dependence of
• thermal mass.

Future Work
finite momentum / gauge dependence / TTc T
gtgtTc full QCD / gluon propagator /